A supermarket display consists of boxes of cereal. The bottom row has 23 boxes. Each row has three fewer boxes than the row below it. The display has six rows.

Write and use a function to determine how many boxes are in the top row. Show your work.

Use the appropriate formula to determine the number of boxes in the entire display. Show your work.

b(r)=23-3r+3

b(r)=26-3r

b(6)=26-3(6)

b(6)=8 boxes in the sixth row...

The sum of boxes will be the average of the top and bottom rows times the number of rows...

6(8+23)/2=93 boxes in total...

Answer Link

facundo3141592 facundo3141592 · Answer 2 · 2022-04-15T14:28:00+02:00

By finding the correspondent function, we will see that there are 8 boxes on the last row and 93 boxes on the entire display.

How many boxes are on the top row?

We know that the bottom row has 23 boxes, and each row after that has 3 fewer boxes.

So we can write the number of boxes per row as:

B(r) = 23 - 3*(r - 1)

We know that the display has 6 rows, then the top row is r = 6, replacing that we get:

B(6) = 23 - 3*(6 - 1) = 23 - 15 = 8

The top row has 8 boxes.

How many boxes are there in total?

Here we need to sum:

T = B(1) + B(2) + B(3) + B(4) + B(5) + B(6)

T = 6*23 - 3*(1 + 2 + 3 + 4 +5)

T = 6*23 - 3*15 = 93

there are 93 boxes in the entire display.

If you want to learn more about functions, you can read:

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